The Sibson and Arimoto capacity, which are based on the Sibson and Arimoto mutual information (MI) of order {\alpha}, respectively, are well-known generalizations of the channel capacity C. In this study, we derive novel alternating optimization algorithms for computing these capacities by providing new variational characterizations of the Sibson MI and Arimoto MI. Moreover, we prove that all iterative algorithms for computing these capacities are equivalent under appropriate conditions imposed on their initial distributions.

翻译：基于{\alpha}阶西布森互信息（MI）和有本互信息（MI）分别推导出的西布森容量和有本容量，是信道容量C的经典推广。本研究通过提供西布森MI和有本MI的新变分表征，推导了计算这些容量的新型交替优化算法。此外，我们证明在对其初始分布施加适当条件的情况下，所有计算这些容量的迭代算法均具有等价性。